Rethinking the Foundations of Statistics

• Introduction; Part I. Decision Theory for Cooperative Decision-Making: 1. Shared preferences of two Bayesian decision makers; 2. Decisions without ordering; 3. A representation of partially ordered preferences; Part II. The Truth about Consequences: 4. Separating probability elicitation from utilities; 5. State-dependent utilities; 6. Shared preferences and state-dependent utilities; 7. A conflict between finitely additive probability and avoiding Dutch book; 8. Statistical implications of finitely additive probability; Part III. Non-Cooperative Decision Making, Inference, and Learning with Shared Evidence: 9. Subjective probability and the theory of games; 10. Equilibrium, common knowledge, and optimal sequential decisions; 11. A fair minimax theorem for 2 person (zero-sum) games involving finitely additive strategies; 12. Randomization in a Bayesian perspective; 13. Characterizations of externally Bayesian pooling operators; 14. An approach to consensus and certainty with increasing evidence; 15. Reasoning to a foregone conclusion; 16. When several Bayesians agree that there will be no reasoning to a foregone conclusion.

"The material is well presented, and the authors themselves have made significant contributions to this area...should greatly appeal to philosophers, advanced graduate students, and researchers interested in exploring and researching the foundations of Bayesian statistics." CHOICE